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OF THE 

MASSACHUSETTS INSTITUTE 
OF TECHNOLOGY 



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Research Program on the 
Management of Science and Technology 

THE TECHNOLOGICAL PROGRESS FUNCTIONr 
A NEW TECHNIQUE FOR FORECASTING- 



Alan R. Fusfeld ' 



January 1970 



#438-70 



MASSACHUSETTS 

INSTITUTE OF TECHNOLOGY 

50 MEMORIAL DRIVE 

CAMBRIDGE, MASSACHUSETTS 02139 



Research Program on the 
Management of Science and Technology 

THE TECfiNOLOGlCAL PROGRESS FUNCTION? 
A NEW TECHNIQUE FOR FORECASTING* 

Alan R. Fusfeld " 
January 1970 #438-70 



-■=Based on a paper read at the annual meeting of TIMS in Atlanta, 
October 3, 1969. This paper is being published in Technological 
Forec asting , Volume 1, Issue 3, Winter 1970. 

The author is a special student at MIT's Sloan School of Management, 
E52-530, 50 Memorial Drive. Cambridge, Mass. 02139, while on 
leave of absence from his senior year at The Johns Hopkins University, 
Baltimore, Maryland. 



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THE TECHNOLOGICAL PROGRESS FUNCTION: 
A NEW TECHNIQUE FOR FORECASTING 

1. BASIC ASSUMPTIONS : 

The core of technological trend forecasting has most 
often been based upon a plot of a technical parameter 
against time. This study concerns the implications for 
forecasting, when these technical parameters are plotted 
against cumulative production. 

For the examples covered in this study, the relation- 
ships between technical characteristics and cumulative pro- 
duction all have the mathematical form: 

Ti = a(i)^ (1) 

where Tj^ = value of parameter at the i^h unit, 

i = cumulative production, 
and a,b = constants. 

This dependence of a technical value upon production is defined 
here as the technological progress function . This paper relates 
the development of that function, the implications of the math- 



4. 

ematical form just mentioned for trend forecasting, and 
information compiled from a variety of case studies.* 

It is of interest to note that the form of the technological 
progress function is similar to that of the common industrial 
"learning curve", as well as the learning curves of psychologists, 
The industrial "learning curve" relates cost to production 
(1, 2, 3) . 

Yi - Yid)"^ (2) 

where y- = cost of the i unit 

i - cumulative production 

st 
y-^ = cost of 1 unit 

b = constant . 

and the psychological learning curve relates the efficiency 

of performing a task to the number of repetitions (4, 5, 6, 7) 

b 



Ejj = k(N) 



(3) 



where 



th 



E„ = efficiency of performing N task 
N = cumulative task number 



k,b = constants 



* Studies completed included: 
civil aircraft-speed 
military aircraft- speed 
turbojet engines- specific weight 
turbojet engines- specific fuel 
consumption 



automobiles- horsepower 
electric lamps- lumens 
computer programs- figure 

of merit 
hovercraft- figure of merit 



5. 



They are similar to the technological progress function, 
T^ = a(i) , because all three show the measure of some 
characteristic, for which improvement is desired, as an 
exponential function of the cumulative number of repetitions 
or production. 

The environment in which technology develops is clearly 
of additional interest and appears to affect the rate of 
learning through discrete changes in the learning constant, 
b. It must be specified here, that environment refers to 
the external economic factors which surround the production 
process. An example of this effect was the change in the 
government investment and market potential relating to the 
automotive industry in the late twenties (8, 9) , which 
multiplied the rate of progress, b, by a factor of 6.2. 



2. INTRODUCTION AND BACKGROUND INFORMATION : 

The development of the technological progress function, 
T^, characteristic of technological improvement, evolved 
from a consideration of: 

(1) problems and background factors inherent in 

industrial progress relationships, 

(2) indications from psychology that general phenomena 

of "learning" were present, 
and (3) difficulties in existing techniques of forecasting. 

2.1 PROGRESS FUNCTIONS : 

Briefly, industrial progress relationships are functions, 
such as production costs/unit, maintenance costs/unit, and 
manufacturing costs/unit, which can be written as a function 
of costs associated with unit number one, the cumulative unit 
number, and a learning constant. They are termed progress 
functions because a reduction in costs indicates a gain in 
efficiency. These functions, as previously mentioned, have 
been found to have the precise form (1, 2, 10, 11): 

yi - a(i)-b (1) 

When plotted on log-log paper, this gives a straight line, 
whose slope, -b, is the rate of progress, that is, the rate 
at which efficiency is improving. It should be noted here 



that, as previously mentioned, the technological progress 
function has the same form and expression, the difference 
being a positive rather than a negative slope. 

Various studies of industrial progress functions have 
shown that there are a number of causes or factors which 
are common to most of the different types (1, 2, 11, 12, 13). 
The more direct factors are: 

1. engineering or desing improvements; 

2. servicing technician progress; 

3. job familiarization by workmen; 

4. job familiarization by shop personnel and engineering 
liason; 

5. development of a more efficient parts upply system; 
and 6. development of a more efficient method of manufacture. 
The innate factors are: 

1. the inherent susceptibility of an operation to improve- 
ment ; 
and 2. the degree to which this can be exploited. 

These functions can be called "micro-economic progress 
functions" (MEPF) because: 

1. they are similar in mathematical form, 
and 2. each relates to decisions of the "firm". 
However, their applicability to development decisions is not 



8. 

as simple as it would seem initially since the functions 
contain two areas of problems. Both areas are relevant 
to the subject of the technological progress function be- 
cause the first helped to prompt its development and the 
second helps to explain its behavior. 

The first area involves certain MEPF characteristics 
which present problems of decision that have been unsolvable 
because of their link with technological innovation. The 
problems begin when one attempts to determine the component 
costs of the first unit of production and finds that one must 
arbitrarily set a limit upon the background development 
expenses. A mechanism by which background and development 
costs would be linked to all of the generations of a product 
might help to alleviate this difficulty of first unit costs; 
of course, this would first require a model for technological 
change. 

Further and more fundamental complications become apparent 
when the development of new generations of equipment is con- 
sidered, as opposed to the difficulties of measuring cost for 
any one generation. Technical changes and design modifica- 
tions are part of the inherent forces that cause the MEPF 
to behave as it does, but there are no provisions for setting a 
limit on these changes; the engineering change procedure of 
firms being arbitrary in nature. That is to say that, after 



a certain number of modifications in production procedure 
or design, the product in reality will be a "new" product 
and will be so labeled by sales and management. This is often 
the case with developments resulting from both conscious and 
unconscious defensive research, which is designed to improve 
a product's competibility . 

The locating of an "old-new" product line or determining 
where a major change begins are questions posed by users of 
the MEPF and seem to beg a progress function which cuts 
across individual generation lines. The technological pro- 
gress function is such a relationship and contains the same 
factors of engineering learning and motivation of the MEPF, 
which not only cause problems in its use but also provide a 
major stimulus for technological advancement. 

The other problem area relates to deviations from normal 
(line a-rity on log-log paper) MEPF behavior. The explanations 
of these differences are important, since they help to clarify 
the effects of external factors of the environment on tech- 
nological progress. Some of these deviations are due 
to changes in the psychological motivation of the personnel 
involved, as would be the case where a product line is sud- 
denly scheduled for discontinuance or where the success of a 
new development is announced to the employees (1, 2, 14). 



10, 



others would be due to changes in design or the introduc- 
tion of new people to the job. Finally, if the product 
or system is being constructed on parallel assembly lines 
or shifts, the addition or subtraction of new lines, perhaps 
with changes in demand, will cause anomalies in the MEPF 
(14). All of these deviations cause a change in the 
slope of the progress function. Thus, it is implied 
that changes in the rate of progress (i.e., the slope of 
the progress function) are not random but are a function 
of critical parameters forming part of the external environ- 
ment. 
2.2 PSYCHOLOGY : 

In addition to the information supplied by analysis of 
progress functions, further insight has been gained from 
psychological learning theory. Since there is considerable 
dispute over exact definitions of what learning is or is not, 
let me point out that, here, psychological learning refers to 
perceptible gains in performing given tasks. These tasks in 
academic studies have ranged from solving puzzles and going 
through mazes to simple studies of response time for given 
stimuli. It has been noted in a variety of projects concerning 
both animals and people, that the efficiency of performing a 



11. 

given tasks increases with the cumulative number of repeti- 
tions (4, 5, 7, 14, 15, 16). It should also be pointed out 
that none of the studies differentiate between the fre- 
quency of the repetitions as long as the frequency was within 
the maximum retention interval. The studies found that, 

Ejj = K(N)^ (2) 

where Ejj = efficiency in performing the N^^ task, 

N - the cumulative task number, 
and K, a = constants. 

Such a relation was particularly apparent in a 1934 study 
with children by Melcher (7) and in a 1955 study with dogs 
by Bush and Hosteller (4) . A similar but different relation- 
ship regarding repetitious activity can be derived from work 
presented by Frank Logan in his book. Incentive (16). Logan 
noticed of his subjects, that they, "...behave in such a way 
as to maximize reward while at the same time minimizing effort." 
Such behavior is not only identical with the aims of man's 
economic endeavors, but is also a causal factor of technological 
progress . Since the progress functions discussed previously show 
a similar dependency on repetition of tasks, it would appear 
that the same type of learning discussed above is involved. 
2. 3 FORECASTING : 

The third area that has contributed to the present develop- 
ment of the technological progress function is technological 



12, 



forecasting. The primary methods already available, such 
as Delphi, trend extrapolation, trend correlation, and 
growth analogy, do not allow for the easy or precise handl- 
ing of environmental factors (17), This provided further 
incentive to find a progress function that would be a6 com- 
petent as other techniques under constant forces and yet 
allow for environmental change. 



13. 

3. TECHNIQUES USED IN ANALYSIS; 

The work involved in investigating and defining the techno- 
logical progress function was completed through two separate 
lines of reasoning. Both paths were developed while taking 
note of: 

(1) an observation, through analysis of the MEPF, that 
the independent variable should be the cumulative production 
number; 

(2) an implication in learning theory that the form of the function 
should be similar to that of the MEPF and the general structure 
characteristic of improvement functions; and 

(3) a need of forecasting techniques for a term through which 
environmental change could be introduced. 

The paths chosen for development are common to most scientific 
endeavors. They were those of theoretical derivation from known 
relationships and empirical model building from real world data. 



14. 



The theoretical side bases itself on the eauivalence, for 
at least certain areas, of the rate of patent output with 
technological /growth or prc^-ress. Through relationships 
derived or shown by Schmookler (l8) and Villers (19), the 
rate of patent output was related to investment and expected 
profit functions. Prom this point, substitutions were made 
from investment/profit functions, denoting technical ad- 
vance. 

The result was a rela.tionship that equated the level of 
technological improvement to a constant multiplied by an 
increasing Quantity dependent function raised to a positive 
exponent , i.e., 

T. = K( f(i) )^ (3) 

th 
where T. = the level of technology at the i unit of 

production, 

f(i) « a function which varies with the production 

number, i, 

and K,c = constants. 



15. 

Although it seemed to substantiate earlier hypotheses, it 
could only be taken as a further indication that this might 
be the correct approach, since it was not precise enough in 
nature to stand by itself. 

The results of the theoretical derivation cleared away 
doubts from the proposed directions of the empirical phase 
of the study. At this stage, it was clear that the work 
should attempt to correlate technological improvement with 
the cumulative quantity of production. In addition, thoughts 
of incorporating the results with other progress functions 
motivated the gathering of data designed for more extensive 
correlations. 

Real data were then sought to provide information on tech- 
nical parameters, production, and costs with background infor- 
mation to be provided where possible. One could then observe 
the behavior of technological parameters with respect to pro- 
duction under the sets of conditions forming the background 
environment. 

However, before describing the case studies and conclusions 
some of the difficulties involved in this work should be pointed 
out. The most difficult problem was that of obtaining accurate 
data, particularly with regard to cost information. This was 



16. 



solved by combining data from several sources and v/here 
possible having the material validated by someone fa .iliar 
with the field. 

Other nroblems arose concerning the choice of tech- 
nical parameters. In this care decisions were made from 
background information and observation of changes in the 
parameter with resoect to cost changes. 
4. F.IJSENTATION OF DATA; 

The empirical studies discussed here verified both the 
preliminary hyootheses and the theoretical derivation and 
were based upon ana.lyses of data regarding the aircraft 
industry, the electric lamp industry, and computer pror^rammmin" . 
4.1 AIRCRAFT DATA : 

The data from the aircraft industry concerned turbo-jet 
engine development over a period of nearly twenty years and 
was synthesized from two Air Force Institute masters theses 
(20,21), sup'oorting information supplied by the Pratt & 
Whitnoy Division of United Aircraft (22), and Aviation I'acts 
and Figures 1958 (23). From these sources, production cost/ 
unit, production by year, ciAmulative production, and trie tech- 
nological parameters were observed. 

The results have shown, in Figure 1, that technological 
progress, as represented by s-ecific weignt ( dry engine weiglit/ 



o 



Figure 1 



TURBO-JET ENGINE CHARACTERISTICS 




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17. 

pounds of thrust) and specific fuel consumption (pounds of 
fuel/hr ./pound of thrust) is log- linear to a logarithmic 
quantity axis, where quantity indicates the cumulative pro- 
duction of engines within the turbo-jet family. It also 
appears that an arithmetic time axis may be used in place of 
a logarithmic quantity axis on many occasions for the same 
accuracy, whenever production undergoes constant percentage 
increases with respect to time*, 
4.2 ELECTRIC LAMP DATA ; 

The Electric lamp industry data was obtained by combing 
information from James Bright ' s book Automation and Manage - 
ment , (24) and Arthur A. Bright ' s book. The Electric Lamp 
Industry , (25) for 60 watt lamps. These sources enabled the 
study to be concerned with technological progress as re- 
presented by the output of the lamp in lumens, production 
by year, and cumulative production. The many development 
changes made it unnecessary to examine each individual generation 
of lamp. 

The results confirm the existence of a technological 
progress function behaving in accordance with the generalized 
MEPF principles. Figure 2, where this is illustrated, actually 



* The bracketed points at the end of the "specific weight" curve were 
obtained from current advertising information of Pratt & Whitney 
presented in Aviation Week during March, 1969. 



pif^ure 2 



ELECTRIC LMP LUMEN OUTPUT 



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18. 

indicates the existence of two rates of progress. One ex- 
tends from 1912 until 1920 and the second from 1920 until 
1940. This would imply that the external environment 
affecting the lamp industry underwent a shift. Since the 
production which had been increasing at a steady 9.39% per 
year throughout the first period concurrently suddenly 
shifted downward to a rate of 2.74% growth at the same tran- 
sition point (Figure 3), it may be concluded that one or 
more changes in the environment increased the value of the 
exponent "b" in the technological progress equation, while 
at the same time decreasing the rate of growth of production. 

fUe 

It IS interesting to note comparison between the progress 
function for lamps as shown in Figure 2 with the more usual 
forecasting method shown in Figure 4. This data substantiates 
a possible claim that forecasting results with an arithmetic 
time axis are as good as they have been because of the substi- 
tution effect. That is, an arithmetic time axis may be sub- 
stituted for a logarithmic quantity axis, when production 
quantities increase in reasonably constant percentages with 
time, as in Figure 3. 
4.3 COMPUTER PROGRAMMING DA TA: 

An additional example has been drawn from a specific 
experience in programming. Data for this example was made 



pi^re 3 



ELECTRIC LAMP PRODUCTION VS TllIB 



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TREND FORECASTING 



Figure 4 



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19. 



available through the help of John Cleckner, a student at The 

Johns Hopkins University. The example represents the rate of 

progress in the development of a single computer program 

developed solely by him under special arrangement with an area 

firm. A figure of merit was determined which would best represent his ow 

aims while developing the program. This figure of merit equals the 

lines of output divided by the running time. The computer pro= 

gram dealt with an estimation of bakery goods to be sold according 

to the day of the week, store, and particular item. 

In an analogy to the development of products, it was 
decided to regard the last best figure of merit (Figure 5) for a 
particular run as the figure of merit to be processed. T|iis may 
or may not be the true figure of merit for that run, but it 
would be an accurate representation of the figure of merit of the 
best program available at any given point in its total development. 

The results illustrate several areas of interest. The 
first is the applicability of the technological progress function 
to the area of programming. There is also the observance of 
different slopes corresponding to different development phases. 
Finally, since the work was done by one person, the analysis indicates 
the possible role of psychological "learning" theory in techno- 
logical progress. 
ADDITIONAL EXAMPLES: 

Other cases studied demonstrated similar technological 



A COMPUTER PROGRAM DEVELOPMENT 



Figure 5 



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20, 



progress functions, that is, linearity on log-log paper 
when the technical progress parameter is plotted against pro- 
duction. Those cases not discussed here are civil aircraft- 
speed, military aircraft-speed, automobile -horsepower , 
hovercraft-figure of merit, and an office machine development- 
figure of merit. 

One could get the impression, from the data just discussed, 
that the trends observed were basically limited to items of 
hardware, but this was not found to be the case, as evidenced 
by studies of the totally different area of agricultural 
efficiency. From information pertaining to the pounds of rice 
produced per acre in Japan over a period of twelve hundred years, 
three log linear trends were noticeable (26,27). The two major 
lines were a "long term" or ancient trend line and a modern 
trend line of much steeper slope. By calculating backwards, 
it was found that they intersected at a period of great external 
change-- the "opening of Japan". The third line was a moderate 
decrease in slope, which prevailed during the period of World 
War II. 



21, 



THE TECHNOLOGICAL PROGRESS FUNCTION : 

Thus, if we assume that Initial studies are correct , 
technological progress functions exist and are of the same 
general nature as other micro-economic progress functions . 
It is then further implied, that technological progress, as 
denoted by a positively increasing function is logarithmically 
linear with respect to a logarithmic quantity axis under con- 
stant external forces. Over periods of time during which 
external forces vary, the slope of the line, that is, the rate 
of progress, may undergo discrete shifts. Such a function is 
denoted as, 

T. = a(i)^, (4) 

1 

where T^ = the value of the technological parameter, 
i = the cumulative production number, 
a = a constant associated with unit number one, 

and b = the rate of progress, a variable, which is a function 
of the external environment. 



22 



5.1 MATHEMATICS : 

A brief glance at the mathematics shows that where b is 

a constant: 

log (Tj_) = b log (i) + log (a) (5) 

and regarding the differential of (5) 

dT-L = b di 

T^ i (6) 

Equation (6) indicates that, b, being constant, the percent- 
age change in a technical parameter is a linear function of 
the percentage change in cumulative production. 
In addition, it should be noted that: 
if i = (constant) e , (7) 

log (i) = Kt + log (constant) (8) 

and di = Kdt . (9) 

i 

Equation (9) represents a percentage change in production as 

a linear function of time, that is, what has been referred to 

as a "substitution effect". 

Where di = Kdt, 
i 

d T^ = bKdt, (10) 

which is the traditional trend forecasting relationship (28) . 

5.2 RATE OF PROGRESS ; 

From analysis of background information involved in the 
work discussed above and current studies, the rate of pro- 



grass, b, has been designated as a function of: 

L/ the effective sii:e of the technical labor force; 
o(, an intelligence factor-average educational level; 
n, , a pre-learning factor-average experience level; 
I, the level of investraent; 

I, the rate of change of the level of investment; 
d, a r.\aturation factor-durability of item-corripatability; 
na, the anticipated raue of change of raarket derriand-slope 
of sales curve; 
and c, tha corrjTiunica'cion or diffusion rate. 
Currently, work is being done to define the exact nature of 
the function just described within the inherent constraints 
that b is greater than, or equal to, 7ero and never infinity and 
that if L,c^, 6, I, or m go to ^ero, then b also goes to ?ero 
6. SUMMARY : 

This study has been concerned with the technological pro- 
gress function. The study proposes that the technological pro- 
gress function may be based on the cumulative production unit 
number on a logarithmic scale, as opposed to the arithmetic time 
series base used for most forecasts. In this form, the techno—- 
logical progress function allows for environmental changes to 
act upon the rate of progress in a precise manner, that is, dis- 
crete changes in the slope of the function. However, it should 
be noted, that no less care must be taken when employing this 



24, 



technique in addition to or instead of existing methods, 
particularly with regard to physical constraints imposed 
upon the system. 
7. FUTURE WORK - 

The technological progress function is a tool to be used 
with other techniques by the foresighted corporate and military 
development planner, who can no longer overlook the effect of 
technological change upon his proposals for future development. 
Although, it is doubtful that a true "Newton's Law" for pre- 
dicting technological advancement will ever be made, it is 
believed that the development of the technological progress 
function is a step towards more effective predictive methods. 

Considerable work remains to be done in exploring the 
nature and anomalies of the technological progress function 
itself. There is, of course, the need for a precise definition 
of the rate of progress function. In addition, there are 
avenues of research concerning macro-economic implications 
and ways in which the function might be of maximum value to 
technologically oriented firms. 



25. 



REFERENCES 

(1) H. Asher, Cost-Quantity Relationships in the Airframe 

Industry . Project Rand-291, July, 1956. 

(2) W, B. Hirschmann, "Profit Prom the Learning Curve", 

Harvard Business Review , Jan-Feb, 1964. 

(3) J. L. Kottler, "The Learning Curve- A Case History In 

Its Application", The Journal of Industrial Engineers , 
AIIE, July-Aug, 1964. 

(4) R. R. Bush, F. Llosteller, Stochastic Models of Learning , 

John V/iley and Sons, Inc., New York, 1955. 

(5) J. Deese, Psychology of Learning , McGraw-Hill, New York, 

New York, 1967. 

(6) C. I. Hovland, I. L. Javis, H. H. Kelley, Communication and 

Persuasion , Yale University Press, New Haven, Conn., 

1953. 

(7) H. T. Melcher, Children's Motor Learning Vv'ith and V/ithout 

Vision , The Johns Hopkins University Ph.D. Dissertations, 

1934, p. 333. 

(8) W. Owen, Automotive Transportation , The Brookings Institutim, 

Washington, D.C., 1949. 

(9) F. Stuart, ed.. Factors Affecting Determination of Market 

Shares in the American Auromobile Industry , Hofstra 
University Yearbook of Business, Series 2, vol. 3, 
New York, October, 1965. 



26. 



(10) J. G. Abramowitz, G. A. Shattuck, Jr., "The Learning Curve", 

IBM Report No. 31.101, 1966. 

(11) J. G. Kneip, "The Maintenance Progress Function", The 

Journal of Industrial Engineers , AIIE, Nov-Dec, 1965. 

(12) R. A. Conway, A. Schultz, "The Manufacturing Progress Function", 

The Journal of Industrial Engineers , AIIE, Jan-5'eb, 1959* 

(13) M. E. Salveson, "Long Range Planning in Technical Industries", 

The Journal of Industrial Engineers , AIIE, Sept-Oct, 1959. 

(14) J. H. Russell, "Predicting Progress Function Deviations", 

IBM Teclinical Report TR 22.446, August 28, 1967. 

(15) C. L. Hull, C. I. Hovland, R.T. Ross, M. Hall, D. T. Perkir^ 

F. B. Fitch, Mathematico-Deductive Theory of Rote Learn- 
ing , Yale University Press, New Haven, Conn., 1940. 

(16) F. A. Logan, Incentive , Yale University Press, New Haven, 

Conn., I960. 

(17) M. J. Cetron, "Forecasting Technology", Science and Technology , 

Sept, 1967. 

(18) J. Schmookler, Invention and Economic Growth , Harvard 

University Press, Cambridge, Mass., 1966. 

(19) R. Villers, Research and Development; Planning and Control , 

Rautenstrauch and Villers, New York, New York, 1964. 

(20) R. E. Burckhardt, Major USAF, ''Cost Estimating Relationships 

for Turbo-jet Engines", masters thesis, GSM/SM/65-3, 
December, IS 65. 



27. 



(21) R. P. Gould, Major USAP, "Turbo-jet Engine Procurement Cost 
Estimating Relationships" , masters thesis, GSM/SM/65-10, 
August, IS 65. 

(2?) N. Turkowitz, letter to author, November 5, 1968. 

(23) Aviation Facts and Figures- 19^8 > American Aviation Publicatit-n 

1958. 

(24) J. R. Bright, Automation and Management , Harvard University, 

Boston, Mass., 1958. 

(25) A. Bright, The Electric Lamp Industry , McGraw-Hill, Nev/ York, 

1949. 

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New York, 1967. 

(27) W. W. Lockwood, The Economic Development of Japan , Princeton 

University Press, Princeton, New Jersey, 1954. 

(28) R. C. Lenz, Jr., "Technological Forecasting, Air Force 

Systems Command, Wright Patterson Air Force Base, 
Ohio, AD 408 085, ASD*TDR^62-414, June, 1962. 



28. 
BIBLIOGRAPHY 

BOOKS 

Almon, C. Jr., The American Economy to 1973 > Harper and Row, 

New York, 1966. 
Automation and Technological Change , The American Assembly at 

Columbia University, Prentice-Hall, Enrlewood Cliffs, 

New Jersey, 1962. 
Ayres, K., Technological Forecasting and Long Range Planninf- , 

McGraw-Hill, New York, 1969. 
Bright, J. R., Research, Development and Technological Innovation , 

Richard D. Irwin, Homewood, 111., 1964. 
Bright, J. R., (ed.) Technological Forecasting for Industry and 

Government , Prentice-Hall Inc., Englewood Cliffs, New 

Jersey, 1968, 
Brown, M. On the Theory and Measurement of Technological Change , 

Cambridge University Press, Cambridge, England, 1966. 
Cetron, W. J., Technological Forecasting - A Practical Approach , 

Gordon and Breach, New York, 1969. 
Hitch, C. J., Roland N. Mokean, The Economics of Defense in the 

Nuclear Age , Harvard University Press, Cambrid;':e, Mass., 1967 
Human Relations in Industrial Research Management, (ed) .^obert 

Teviot Livingston, Stanley H. Milberg, Columbia University 

Press, New York, 1957. 



29. 



Ma.nsfield, E., The Economics of Technological Change , W. W. 

I 

Norton and Co., New York, 1968. 

Mansfield, E., Industrial Research and Technological Innovation , 

W. W. Norton and Co., New York, 1568. 
Quinn, J. B. , Yardsticks for Industrial Research , The Ronald 

Presc Co., New York, 1959. 
Schon, D. A., Technology and Change , Delacorte Press, New York, 

1967. 
Servan-Schreiber, J. -J., The American Challenge , Athenum, New 

York, 1968. 
Technological Innovation and Society , ed. Dean Morse, Aaron \V. 

Warner, Columbia University Press, New York, 1966. 



30. 



ARTICLES 



Bright, J. R., "Can We Forecast Technology?", Industrial 
Research , March 5, 1968. 

Cetron, M. J. ,R.J. Happel, W.C. Hodgson, W.A. McKenney, T.I. Monahan, 
"A Proposal for a Navy Technological Forecast", Naval 
Material Command, Washington, D.C. 
Part I- Summary Report AD 65919 9 
Part II- Back Up .{eport AD 659 200 May 1, 1966. 

Cetron, M. J., A. L. V/eiser, "Technological Change, Technological 
Forecasting, and Planning R&D, A View Prom the R&D 
Manager's Desk", The George Washington University Law 
Review , Vol. 36, No. 5, July, 1968. 

Darracott, H.T., M.J. Cetron et al, "Report on Technological Fore- 
casting", Joint Army Material Comrn and/Naval Material 
Command/ Air Force Systems Command, Washington, D.C, 
AD 664 165, June 30, 1967. 

Duranton, R. A., "Quelques Remaroues Sur Les Courbes D ' Accoutumance" , 
Internal IBM Report, May 13, 1965. 

Mahanti, B., "Progress Report/Manufacturing Progress Function 

Report", Internal IBM paper (German Office), April 9, 1964. 

"The Growth Force That Can't Be Cverlooked", Business Week , 
McGraw-Hill, New York, August 6, I960. 



31^ 



"The Dynamics of Automobile Demand", General Motors Corp., 

New York, 1939. 
Technology and World Trade , US Department of Commerce, NBS Misc. 

Pub. 284, (symposium — 11/16, 17/66) . 



ACKNOWLEDGEMENTS 

The author offers special thanks to John Cleckner, Class of 1970, 
The Johns Hopkins University, for his suggestions and help in prepar- 
ing the data on computer programming. The author is also indebted 
to Lisa Geiser, Class of 1972, Goucher College and Nancy Smith, 
Class of 1972, Goucher College for their help in developing additional 
data. In addition, Norman Turkowitz of Pratt and Whitney must be 
noted for supplying the supporting information for the aircraft 
engine study, for which the author is also very grateful. 



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